Solving ../../benchmarks/smtlib/true/plus_le_le.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)
}
eq_nat(_mva, _nva) <= plus(_kva, _lva, _mva) /\ plus(_kva, _lva, _nva)
)
(le, P:
{
le(z, s(nn2)) <= True
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
False <= le(s(nn1), z)
False <= le(z, z)
}
)
}

properties:
{
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)
}


over-approximation: {plus}
under-approximation: {}

Clause system for inference is:

{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}


Solving took 0.159953 seconds.
Yes: |_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(z, z) <= True
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005508 s (model generation: 0.005459,  model checking: 0.000049):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
Yes: {

}

plus(n, z, n) <= True  :
Yes: {
n -> z
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 1, which took 0.005950 s (model generation: 0.005893,  model checking: 0.000057):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(z, s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(_gorba_0)
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_iorba_0)
}

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
Yes: {
_jva -> z  ;  mm -> z  ;  n -> z
}


-------------------------------------------
Step 2, which took 0.007061 s (model generation: 0.006993,  model checking: 0.000068):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
Yes: {
_jva -> s(_qorba_0)  ;  mm -> z  ;  n -> s(_sorba_0)
}


-------------------------------------------
Step 3, which took 0.010701 s (model generation: 0.010578,  model checking: 0.000123):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
le(z, z) <= le(s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
  le(z, z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_torba_0)  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
Yes: {

}

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 4, which took 0.015403 s (model generation: 0.015260,  model checking: 0.000143):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
le(s(z), z) <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(z, z)
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(s(x_0_0), z) <= True
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
Yes: {

}

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
Yes: {
_ova -> s(z)  ;  m -> s(_gprba_0)  ;  n -> s(z)
}

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 5, which took 0.009332 s (model generation: 0.009164,  model checking: 0.000168):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_1_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
Yes: {
_ova -> s(s(z))  ;  m -> s(z)  ;  n -> s(s(z))
}

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 6, which took 0.008944 s (model generation: 0.008774,  model checking: 0.000170):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
le(s(s(z)), s(s(z))) <= le(z, s(s(z))) /\ plus(s(s(z)), s(z), s(s(z)))
False <= le(z, z)
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
Yes: {
_jva -> s(z)  ;  mm -> z  ;  n -> s(s(z))
}


-------------------------------------------
Step 7, which took 0.014574 s (model generation: 0.014470,  model checking: 0.000104):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
le(s(s(z)), s(s(z))) <= le(z, s(s(z))) /\ plus(s(s(z)), s(z), s(s(z)))
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  _r_1(s(x_0_0)) <= True
  le(s(x_0_0), s(x_1_0)) <= _r_1(x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_bsrba_0)  ;  nn2 -> s(z)
}

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 8, which took 0.014783 s (model generation: 0.014269,  model checking: 0.000514):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, s(s(z))) /\ plus(s(s(z)), s(z), s(s(z)))
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(z, z) <= True
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(s(_ltrba_0))
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
No: ()


-------------------------------------------
Step 9, which took 0.022576 s (model generation: 0.022414,  model checking: 0.000162):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, s(s(z))) /\ plus(s(s(z)), s(z), s(s(z)))
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= True
  _r_1(z, z) <= True
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0, x_1_0) /\ le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
Yes: {
_jva -> s(s(_uurba_0))  ;  mm -> z  ;  n -> s(s(_turba_0))
}


-------------------------------------------
Step 10, which took 0.022569 s (model generation: 0.022392,  model checking: 0.000177):

Clauses:
{
le(z, s(nn2)) <= True -> 0
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova) -> 0
False <= le(z, z) -> 0
plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva) -> 0
}

Accumulated learning constraints:
{
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= le(s(s(z)), s(s(z)))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, s(s(z))) /\ plus(s(s(z)), s(z), s(s(z)))
False <= le(z, z)
plus(s(s(z)), s(z), s(s(z))) <= plus(s(s(z)), z, s(z))
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= True
  _r_1(z, z) <= True
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

le(z, s(nn2)) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

le(n, _ova) <= le(z, m) /\ le(z, n) /\ plus(n, m, _ova)  :
No: ()

False <= le(z, z)  :
No: ()

plus(n, s(mm), s(_jva)) <= plus(n, mm, _jva)  :
Yes: {
_jva -> s(s(z))  ;  mm -> z  ;  n -> s(s(s(z)))
}


Total time: 0.159953
Learner time: 0.135666
Teacher time: 0.001735
Reasons for stopping: Yes: |_
name: None

le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(z, z) <= True
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|